Moyes said: "Look, it comes to down to winning and in the main over the four years, we've won.
"We've had much more success than negatives. We've had our days when we've been knocked out of cups when we shouldn't have. We've had our days when we lost heavily, as we have a couple of times this season, but overall over the last four-and-a-half years we've made progress.
"I think it's got a much higher profile than it probably did a long time ago. Instead of 60,000, we've got 62,000. There are a lot more young supporters and that's what I see.
"I think all those things are progress and the Club will have to build up and keep going.
"There are lots of challenges in the Premier League because of the big money at some of the clubs and we're probably not one of the clubs in that category, so over the four years we've actually challenged pretty well.
"The reception I got touched me.
"You hear a lot of noise and I'm a football supporter as well and I want my team to win, but like I said, most of the supporters in the stadium recognise that their team won more than it lost.
"That's helped us get strong positions in the league and let's hope we can keep it going."